Copyright © Cengage Learning. All rights reserved.

Slides:



Advertisements
Similar presentations
MA Day 67 April 22, 2013 Section 13.7: Stokes’s Theorem Section 13.4: Green’s Theorem.
Advertisements

VECTOR CALCULUS VECTOR CALCULUS The main results of this chapter are all higher-dimensional versions of the Fundamental Theorem of Calculus (FTC).
Stokes’ Theorem Divergence Theorem
Chapter 16 – Vector Calculus 16.9 The Divergence Theorem 1 Objectives:  Understand The Divergence Theorem for simple solid regions.  Use Stokes’ Theorem.
Copyright © Cengage Learning. All rights reserved. 15 Multiple Integrals.
Copyright © Cengage Learning. All rights reserved. 16 Vector Calculus.
Logarithmic, Exponential, and Other Transcendental Functions Copyright © Cengage Learning. All rights reserved.
Copyright © Cengage Learning. All rights reserved. 16 Vector Calculus.
Copyright © Cengage Learning. All rights reserved. 4 Integrals.
Copyright © Cengage Learning. All rights reserved. Logarithmic, Exponential, and Other Transcendental Functions.
Multiple Integration 14 Copyright © Cengage Learning. All rights reserved.
5 Copyright © Cengage Learning. All rights reserved. Logarithmic, Exponential, and Other Transcendental Functions.
Integration Techniques, L’Hôpital’s Rule, and Improper Integrals 8 Copyright © Cengage Learning. All rights reserved.
Multiple Integration Copyright © Cengage Learning. All rights reserved.
The Fundamental Theorem of Calculus is appropriately named because it establishes connection between the two branches of calculus: differential calculus.
Copyright © Cengage Learning. All rights reserved. 15 Multiple Integrals.
Copyright © Cengage Learning. All rights reserved Change of Variables in Multiple Integrals.
The Fundamental Theorem of Calculus is appropriately named because it establishes connection between the two branches of calculus: differential calculus.
Chapter Five Integration.
Copyright © 2008 Vista Higher Learning. All rights reserved. 9.
Copyright © Cengage Learning. All rights reserved.
Copyright © Cengage Learning. All rights reserved.
Copyright © Cengage Learning. All rights reserved.
Copyright © Cengage Learning. All rights reserved.
Copyright © Cengage Learning. All rights reserved.
Copyright © Cengage Learning. All rights reserved.
Copyright © Cengage Learning. All rights reserved.
Copyright © Cengage Learning. All rights reserved.
Copyright © Cengage Learning. All rights reserved.
4.4 The Fundamental Theorem of Calculus
Copyright © Cengage Learning. All rights reserved.
Copyright © Cengage Learning. All rights reserved.
Copyright © Cengage Learning. All rights reserved.
Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. {image}
Copyright © Cengage Learning. All rights reserved.
Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. {image}
Copyright © Cengage Learning. All rights reserved.
Copyright © Cengage Learning. All rights reserved.
Copyright © Cengage Learning. All rights reserved.
Derivatives and Integrals of Vector Functions
Copyright © Cengage Learning. All rights reserved.
Copyright © Cengage Learning. All rights reserved.
Copyright © Cengage Learning. All rights reserved.
Copyright © Cengage Learning. All rights reserved.
Copyright © Cengage Learning. All rights reserved.
Change of Variables in Multiple Integrals
Copyright © Cengage Learning. All rights reserved.
Copyright © Cengage Learning. All rights reserved.
The Fundamental Theorem of Calculus
Copyright © Cengage Learning. All rights reserved.
Sec 5.3: THE FUNDAMENTAL THEOREM OF CALCULUS
Copyright © Cengage Learning. All rights reserved.
Copyright © Cengage Learning. All rights reserved.
Copyright © Cengage Learning. All rights reserved.
The Fundamental Theorem of Calculus
Copyright © Cengage Learning. All rights reserved.
Copyright © Cengage Learning. All rights reserved.
Copyright © Cengage Learning. All rights reserved.
Copyright © Cengage Learning. All rights reserved.
16 VECTOR CALCULUS.
Copyright © Cengage Learning. All rights reserved.
Copyright © Cengage Learning. All rights reserved.
Copyright © Cengage Learning. All rights reserved.
Copyright © Cengage Learning. All rights reserved.
Copyright © Cengage Learning. All rights reserved.
Copyright © Cengage Learning. All rights reserved.
Copyright © Cengage Learning. All rights reserved.
Copyright © Cengage Learning. All rights reserved.
Chapter 5 Integration.
Copyright © Cengage Learning. All rights reserved.
Presentation transcript:

Copyright © Cengage Learning. All rights reserved. 16 Vector Calculus Copyright © Cengage Learning. All rights reserved.

Copyright © Cengage Learning. All rights reserved. 16.10 Summary Copyright © Cengage Learning. All rights reserved.

Summary We collect all higher-dimensional versions of the Fundamental Theorem of Calculus together here (without hypotheses) so that you can see more easily their essential similarity. Notice that in each case we have an integral of a “derivative” over a region on the left side, and the right side involves the values of the original function only on the boundary of the region.

Summary cont’d

Summary cont’d